Asymptotic Solution for the Low-Thrust Restricted Two-Body Problem

A semi-analytical solution of the restricted two-body problem subject to an arbitrary low thrust is developed. The multiple scales perturbation method is used to split the problem into “slow” and “fast” scales. The small parameter that permits this approach is the ratio between thrust and gravitational acceleration. The thrust is expressed as a Fourier series expansion in terms of the fast scale, in which the coefficients are allowed to vary in the “slow” scale. The spectral analysis of the equations of motion gives rise to reduced dynamics of the “slow” motion. The results of the integration of this dynamical model are validated against the integration of the complete dynamics. Moreover, the preliminary results show that the propagation of the reduced dynamics are comparatively much more efficient than the complete dynamics, and show also t expected small errors of the method.